Directional microphone with a compliant link interconnected between the two diaphragms



- BAUER 2,553,539 DIRECTIONAL MICROPHONE WITH A COMPLIANT LINK INTERCONNECTED BETWEEN THE TWO DIAPHRAGMS Filed June 16, 1947 2 Sheets-Sheet 1 May 22,- 1951 INVEN TOR. 5 W ,6. 49am- JM zkwwafi May 22, 1951 B. B. BAUER DIRECTIONAL MICROPHONE WITH A COMPLIANT LINK INTERCONNECTED BETWEEN THE TWO DIAPHRAGMS Filed June 16, 1947 2 Sheets-Sheet 2 Patented May 22, 1951 DIRECTIONAL MICROPHONE WITH A COMPLIANT LINK INTERCONNECTED BETWEEN THE TWO DIAPHRAGMS W Benjamin B. Bauer, Oak Park, Ill., assignor to Shure Brothers Inc., Chicago, 111., a corporation of Illinois Application June 16, 1947, Serial No. 754,798

24; Claims. (01. 179- 139) This invention relates to apparatus for the conversion of wave motion of one character into wave motion of diiferent character, such for example as changing sound waves into electrical waves in microphones and the converse in loud speakers. ratus of this character which is of a directional nature, i. e., the instrument is active preferentially in one or more directions throughout an extensive range of frequencies and is relatively inoperative or less operative in other directions, it being anobject of the invention to provide improved apparatus of this character.

While the invention is disclosed and described in connection with microphones, it will be understood by those skilled in this art that it may also be applied to sound reproducing means such as loud speakers Without departing from the spirit and scope of the invention. i

In many acoustical applications, it is desirable or necessary that a, microphone have directional properties. For example, in a public address system involving the use of a microphone and one or more loud speakers the sound emanating from the loud speakers may, by one or more reflections, be transmitted to the microphone and hence pass through the amplifying system with resulting disturbances. Similarly in an instance where there are numerous sounds present in addition to the voice of an announcer, as for example an announcer speaking from a crowded room or platform where the announcers voice may have very littlemore intensity than the voices of the people surrounding him, the sound picked up by the microphone will have a large number of extraneous components in it. In these instances, if the microphone is directional such that it discriminates very largely in favor of sounds coming to it from a particular area, from directly in front, for example, the amount of extraneous sound passing through the system will be much decreased. Itis well known to construct microphones of a unidirectional character having a pair of transducing elements, one of which is responsive to the pressure component of a sound wave and another of which is responsive to the pressure gradient of a sound wave, the outputs of the two transducers being combined by means of an electrical network. Microphones having directional characteristics may be constructed by using a single transducing element which is arranged to have two sound stimuli transmitted to it, the two stimuli being derived from the same functional component of a sound wave but with an acoustical network combining them. Such microphones More particularly, it relates to appa- 2 may be constructed with different directional characteristics through a suitable choice of design constants as well-as units whose directional characteristics may be varied by proper manipulation of their structure. Thus one may construct a unit having maximum response from the front and zero response from the rear or one hundred and eighty degrees displaced therefrom, this being the cardioid type of response; a unit having maximum response from the front and rear or one hundred and eighty degrees displaced from each other and zero response at right angles, this being the bidirectional or cosine law type of response; a unit having maximum response from the front, a lesser but not zero response from the rear, and zero or greater than zero response from some other direction; a unit having no directivity; or a unit whose directional characteristic may be varied from any one of the foregoing patterns to any other one.

It is a further object of the invention to provide an improved directional sound translating device eliminating electric circuits interconnecting the transducing elements.

It is a further object of the invention to provide an improved directional sound translating device comprising a pair of sound translating elements coupled by compliant means.

It is a further object of the invention to provide an improved directional sound translating device comprising a pair of sound translating elements coupled by impedance means.

It is a further object of the invention to provide an improved sound translating device with a directional response pattern obtained 'by the action of sound wave effects at two points in a sound wave and compliant means coupling the sound wave effects on a single transducing element.

It is a further object of the invention to provide, in a directional sound translating device embodying a pair of flexibly supported diaphragms coupled by compliant means, improved means for compensating for the diaphragm supporting or edge stiffness over the useful frequency range.

It is a further object of the invention to provide an improved type of network interrelating the sound wave eifects obtained from two points in a sound wave which is relatively unaffected by atmospheric pressure and temperature.

In carrying out the invention in one form, a directional sound translating device is provided comprising a pair of spaced apart diaphragms adapted to vibrate, means for transforming the vibrations into electrical variations, compliant 3 means interrelating the vibrations of the diaphragms for producing a resultant vibration, and means for transmitting the resultant vibration to the transforming means. More particularly, the compliant means may include gaseous as well as mechanical elements singly or in combination.

For a more complete understanding of my invention, reference should now be had to the accompanying drawing in which:

Figure 1 is a sectional elevational view of a microphone embodying my invention;

Fig. 2 is a diagram of forces for the microphone of Fig. 1 for sound of front incidence;

Fig. 3 is a similar diagram of forces for sound of rear incidence;

Fig. 4 is a similar diagram of forces for sound of right angle incidence;

Fig. 5 is a sectional elevational view of amo'dified form of the invention;

Fig.6 is a diagram of forces for the microphone of Fig. 5 for sound of front incidence;

Fig. '7 is anelectrical circuit analogous to the structure of Fig. 1 for explaining the operation of the invention;

Fig. 8 is a series of polar patterns indicating the different response patterns of the microphone obtainable according to the invention;

Fig. 9 is a fragmentary sectional view of a modified form of the invention shown in Fig. 1;

Fig. 10 is a fragmentary sectional view of another modified form of theinvention shown in Fig. 1;

Fig. 11 isa sectional elevational view of anotherembodiment of the invention;

Fig. 12 is a sectional elevational view of another embodiment of the invention;

Fig. 13 is a diagram of forces for sound of rear incidence'for the embodiment of Fig. 12;

Fig. 14 is an equivalent electrical circuit diagram analogous to the structure of Fig. 12 for explaining the operation of the invention embodied in Fig. 12; and

Fig. 15 is a fragmentary sectional view of another modified form of the invention.

Certain subject matter relating to mechanical damping means for diaphragms shown in the various figures is claimed in the continuation-inpart application Serial No. 222,747, Benjamin B. Bauer, entitled Mechanical Damping Means for the Diaphragms of Microphones, Speakers and the Like, filed April 25; 1951.

Referring more particularly to the drawings, the invention is shown in'Fig. 1 as comprising a microphone including a pair of diaphragms I8 and II adapted to vibrate and separated from each other by a distance d. The diaphragms may be made of any suitable material, such as thin aluminum or paper, for example, and are generally conical or curved in form so as to be relativelystiii whereby the diaphragms, in their movements, act largely as pistons. At their edges the diaphragms are resiliently supported and form the closures for casings l2 and I3 made of any sound impermeable material, casings I2 and I3 being separated from each other and relatively rigidly held together by means of spacers I4 thereby holding diaphragms I0 and II' spaced apart. Diaphragms l0 and II are placed opposing each other for a purpose to be described subsequently in this specification. This spacing may vary and in some instances the spacers I4 may be eliminated to provide a common wall between casings I2 and I3. A circular case may surround casings I2 and I3 to minimize perturbations of the sound field. Diaphragm III with casing I2, and diaphragm II with casing I3 define cavities or chambers I5 and I6 filled with air, diaphragm II being shown larger in area than diaphragm IO to compensate for the stiffness of diaphragm II, but it will be made clear that under certain conditions the diaphragm areas may be equal. The case 20, as well as cavities I5 and I6, may be provided, if needed, with a small or high resistance vent 20a, I51: and Ilia to the atmosphere to equalize the inside and outside pressure.

At the center or apex of diaphragm I8, a drive unit I l is firmly attached by cementing, for example, the drive unit extending through an opening in the rear of casing I2, which opening is sealed by as'eal I8 made of rubber, paper, or some other flexible material which will permit small mechanical vibrations of the drive unit without allowing sound waves to enter cavity I5. Similarly, a drive unit I9 is firmly attached to the center or apex of diaphragm II, the drive unit extending through an opening in the rear of casing I3 which opening is sealed by a seal 2i also permitting small vibrations of the drive unit without permitting sound waves to enter cavity It. The rear ends of drive units II and I9 are brought relatively close to each other and are joined by means of a compliant link 22 made of some springy material such, for example, as rubber, mechanical springs or one of the compounds known as elastomers. Consequently diaphragms I0 and II are not rigidly but resiliently connected to each other, and vibrations of one diaphragm are transmitted to the other as modified in one respect by compliant link 22. Stationarily fixed to the rear of casing I3 within cavity I6 there is a damping or dissipative element 23 attached to drive unit It so as to move therewith and introduce a resistance to the motion thereof, the dissipative element being made, for example, of the compounds known as elastomers. Many elastomers have the ability to absorb energy as well as springiness and hence may combine dissipation with compliance, examples of suitable elastomers being materials available as Viscoloid and Flexiglass. In the event that an elastomer is used for link 22, the diaphragms are coupled by an element having both compliance and dissipation and thus are coupled by an impedance.

In order to derive an electrical output from the movements of the diaphragms, a piezoelectric crystal 24 is mounted inside of cavity l5 and is relatively rigidly connected at one end through a collar 25 to drive unit I! whereby movements of drive unit I1 produce deformations of the crystal with a resultant voltage output. Conductors 26 and 21 extending from crystal 24 lead outwardly through casing I2 for supplying the voltage generated to a suitable amplifier or other apparatus.

Spaced directly in front of diaphragm I0 is an acoustical screen 28 which may be constituted of a suitable wire screen support having one or more thicknesses of cloth thereon forming acoustical resistance and inertance, screen 28 being spaced from diaphragm l0 and defining therewith a cavity or volume 29.

Assuming that the structure of Fig. 1 is placed in air and sound waves approaching in the direction of the arrow A impinge thereon, the sound waves will come into contact with screen 28 and after a slight delay will contact diaphragm I0. At some instant later, determined by the efiective distance d between screen 28 and diaphragm I I, and the sound frequency, the sound waves will come into contact with. diaphragm II. The effective distance d differs from the linear distance between screen 28 and diaphragm I I because sound waves must bend around the barriers provided by the casings, the effective distance being greater. Because of this eifect the sound wave pressures across the screen 28 and diaphragm H are not' constant. Consequently, the effective distance d is equal to the distance d plus an average oreffective distance from the edges of the structure to the apex of diaphragm II and screen 28. In instances where the distance d is relatively small compared to the diameters of the casing, the effective distanced may approximate three quarters of the distance from the center of screen 28 and the center of diaphragm ll. As the distance d increases relative to the casing diameter, the effective distance approaches the center to center distance and becomes very nearly equal to it for large valuesof d. A sound wave, being in one aspect thereof a varying pressure wave traveling through the air, exerts varying pressure when it contacts it through collar 25, is the resultant of two forces.

' pliant link 22, itbeing necessary to place the the diaphragms, the sound pressurebeing converted into a mechanical force thereby. Sound pressure waves contacting diaphragm l0, after permeating the screen 28, will cause this diaphragm to exert a mechanical force, on crystal 24, the phase of'this force being determined by the resistance and inertance of screen 28 and the compliance of cavity 29, since the combined mass of the diaphragm and its drivegunit, its mechanical resistance to movement or friction, the stiffness of the diaphragm mounting as well as the stiffness or resilienceof the air within cavity l5 are sufficiently small compared to corresponding characteristics of the crystal thatthey may be considered part thereof. .Sound pressure waves contacting diaphragm ll exert a force thereon. This mechanical force is shifted in phase by the combined mass of diaphragm II and driveunit I9, its resistance to movement or friction, the stiffness of the diaphragm mounting, the stiffness of the air within cavity 16, the damping or resistance of dissipative element 23, and the com 'pliance of link 22, link 22 serving to transmit a function of this force to crystal 24. The effects of seals l8 and 2| are made negligible.

A directional microphone discriminates in favor of sound coming from a particular direction or directions. One form of such directivity and the one treated in detail in the following paragraphs is the'one in which a microphone has maximum response where sound falls on it directly from the front (direction of arrow A),

has minimum or zero response where sound falls on it directly from the rear (direction of arrow B), and has a response varying between maximum and zero where sound falls on it from directions in between front and rear (1. e., cardioid response of Fig. 8, 7c=1). In the microphone shown in Fig. 1 the response thereof for any direction of sound incidence .is'the voltage generated by crystal 24 for sound of thatdirection. The voltage generated by a crystal being proportional to its deformation, and since its deformationis proportional to the applied force, the cardioid form of response is obtained when the force acting on crystal 24 through collar 25 is a maximum for front sound incidence, is zero for rear sound incidence, and has values interme-' maximum and zero for'intermediatedirecof sound incidence.

force acting on crystal 24, transmitted to 1 ing directly therefrom oppose each other.

to crystal 24, only after having its phase shifted by a phase shift network including mechanical damping of element 23, the mechanical mass of diaphragm H and drive unit 19, the resilience (compliance) of the .air within cavity J6, the. resilience (compliance) of mounting of diaphragm l I, and the resilience of link 22. To produce zero response for sound of rear incidence, the force from diaphragm l5 and the force transmitted through link 22 must be equal in value and opposed to each other.

The functioning of the various elements to produce the necessary forces which, when combined to act on crystal 24 for producing cardioid or unidirectional response, may best be understoodby considering the force diagrams Figs. 2, 3 and 4 in connection with Fig. 1.

Considering first Figs. 1 and 2 (normal front incidence of sound waves as indicated by the direction of arrow A), sound of pressure P falling upon screen 28 will pass therethrough and fall on diaphragm if! to exert a pressure P1 thereon giving rise to a force E1 equal to the product P1A Where A is the area of diaphragm [0. The characteristics of screen 28 and cavity 29 are chosen as subsequently pointed out so that the numerical values of P1 and P are equal throughout a substantial frequency range. Screen 28 and cavity 29 produce a phase shift designated by the angle a between the sound pressure in front of screen 28 and the sound pressure exerted on diaphragm [0. Henc the force E available in front of screen 28 may be considered to be PA and is equal to the force B1,. differing only in phase throughout the unidirectional range of the network. This same sound wave, .before reaching diaphragm H, travels the effective distance d through the atmosphere to exert a pressure P on diaphragm l I giving rise to the force E" equal to the product PA where A is the diaphragm area. The force E differs in phase angle from the force E by from diaphragm ll may be designated E1 and differs from E by a phase angle made (or designed to be) equal to the sum of the phase angles introduced by screen 28 and cavity 29, and the effective distance d, i. e. (|a) produced by the phase shifting network. The angle (o-i-a) may be termed the internal phase angle. The force E1 is also less than the force E or E since a portion of the force E is consumed in deforming diaphragm II and compressing the air in cavityz lfi. .Ei is made equal to force E1 7 a. proper choiceof. diaphragm areas as. will be pointed out subsequently in this specification. The resultant vector combination of E1 and E1 designated as Er acts on crystal 24 to produce the voltage output or response.

Considering next Figs. 1 and 3 (normal rear incidence of sound Waves as indicated by the direction of arrow B), the force on diaphragm ll due to the sound pressure is E and has a magnitude the same as in Fig. 2. Due to the time necessary for this sound wave to travel the effective distance d to screen 28, the force E available there difiers from source E by an angle equal in value to that in Fig. 2 since sound is traveling the same distance d, the forces E in the two figures being also equal in magnitude since the same instrument is involved. The relative position of E and E in the two figures is reversed since sound strikes the rear diaphragm first for rear sound incidence. The sound Waves after striking screen 28 pass therethrough and exert a pressure on diaphragm ll) giving rise to the force E1 which difiers from force E by the phase angle a. In Fig. 3 also, since the diaphragms are opposed in direction, the force E is reversed to E. The force E1 transmitted to drive unit I? from diaphragm ll difiers from force E by a phase angle |a, equal in value to that of Fig. 2, produced by the phas shifting network. Since E1 is at an angle (+a) clockwise from E, and E1 is at an angle (+a) clockwise from E, E1 and E1 are opposed to each other and since they are equal in magnitude due to a proper choice of diaphragm areas the resultant force on crystal 2% is zero. Hence for rear sound incidence the microphone has zero response.

Fig. 4 shows the force diagram for an instance where sound falls on the microphone from the side or at right angles to directions A and B. Since the sound in this case strikes the screen 28 and diaphragm II at the same time, the phase angle between the forces E and E is zero, E being greater than E as previously. Due to screen 28 the force E1 has a phase angle a relative to force E. The. force E is reversed to -E and the force E1 has a phase angle (girl-a) which has the same value as for Figs. 2 and 3, relative to force E since the sound in passing through the network experiences the same phase shift irrespective of the direction of sound incidence. Combining E1 and E1 vectorially, the resultant Er gives the force tending to deform crystal E i or the microphone response for this direction of sound incidence. Comparing Er from Figs. '2, 3 and 4, it is evident that the response for front incidence is greatest, and that for right angle incidence has a value between this and zero.

By constructing a series of force, diagrams for different directions of sound incidence the total response may be obtained, the phase angle 5 between the forces E and E or between any two points in a sound wave spaced apart by an effective distance :1 being givenby the expression cos 0 where Cwi$th6106it of the sound wave in centimeters per second;

a is the angle; between the incident sound and normal. front incidence (the direction of arrow A).

Since the velocity of sound is a constant under fixed atmospheric conditions, no is a constant for somearbitrary frequency and 01 may be fixed in the microphone construction, it is evident that the phase angle e is proportional to cos 0. For 0 equal to zero, 1. e. sound is incident directly from the front cos 6:1 and the phase angle equals ill and is amaximum (Fig. 2). If sound approaches the microphone from a direction at right angles to arrow A, 0 is ninety degrees and cos 0 is equalto zero. Consequently 5 is equal to zero. This is equivalent to saying that the sound contacts screen 28 and diaphragm II at the same time and is shown in Fig. 4 where E and E li along the same direction. For sound of rear incidence cos 180 is equal to 1. Hence cud This is evident in Fig. 3:since E is rotated clockwise-from E which is the reverse of Fig. 1. By constructing a series of force diagrams, as indicated for Figs. 2, 3 and 4, with E having different angularities relative to E determined by the expression cos 0 the complete microphone response may be determined which will show that for directions of sound incidence intermediate front and rear, the response of the microphone will be between maximum and zero and will have the shape of a cardioid.

The presence of screen 28 having acoustical inertance and resistance and cavity 29 having acoustical compliance are. not necessary for unidirectional operation of thedevice and may be omittedin some embodiments if appropriate adjustment of the phase shifting network constants are made. Fig. 5 illustrates one example of such a microphone, andFig. 6 is the force diaphragm or sound of a given, incidence. (In Fig. 5 screen 39,, 41 produces the effect produced by member 23; of Fig. 1.) Thus, when screen 28 is omitted from Fig. 1 sound approaching from the front contacts. diaphragm I0 directly and E. becomes coincident with or the same thing as E1 (angle a=O). Then the phase angle between E and E is equal to and the phase angle between E and E1 determined by the phase shift network is and is made equal to The vector diagram of Fig. 6 illustrates this situation where E is the force of sound incident on diaphragm [0, E is the force of the sound wave incident on diaphragm I l and is shifted with respect to Ev by an an le w 2.5 centimeters.

E and E is equal to l C, for front incidence, is equal to e Z I for rear incidence, and is zero for right angle incidence. Since the phase angle between E' and E1 is now instead of cod ef it is seen that removing screen 28 necessitates that the phase shifting network components of mass, dissipation and compliance must have their values adjusted to produce the smaller phase shift required.

Since the distance between diaphragms may be fixed in any microphone and the velocity of sound is a constant, it is evident from the expression for phase angle cod r between two points in a sound wave that for any direction of sound incidence the phase angle is 1'0, pliance of cavity l5 may in general be thesame as for the rear diaphragm and cavity but for the analysis used above were assumed combined with the mass and compliance of the crystal. 4 The operation of my invention may be explained in greater detail and the value of the constants determined by considering the various elements of the microphone as analogous to certain circuit elements of an electrical circuit." In' presenting these analogues it is customary to treat acoustical mass (interance) and mechani cal mass as if they were electrical inductances; acoustical and mechanical compliances as if they were electrical capacitances; and acoustical and mechnical resistances (fluid friction) as if they were electrical resistors. In the conventional analogues the equivalent electrical circuit may be in either the mechanical or acousticalizconstants of the network. When various acoustic elements are associated with a single diaphragm, the mechanical constants of all elements are ob tained from acoustical constants by multiplying the acoustic impedance of all acoustic elements by the square of the area of thediaphragm. all the following circuit constants, acoustical units for mass are grams cm.- for resistance, cm. sec.- dynefor compliance, cm. dyne- Mechanical units for mass are grams; for resistance, cm. sec.- dyne- ;,for compliance, cm. dyne- Corresponding electrical circuit elements are in henrys, ohms, and farads. In Fig. 7 the equivalent electrical circuit for the micro: phone of Fig. 1 is shown in terms of mechanical circuit elements. The acoustic resistance, and inertance of screen 28, R and L in series multiplied by the square of the diaphragm area, correspond to electrical resistance and inductance in ohms and henrys respectively. The mechanical compliance reflected upon the diaphragm 10 by dependent on the frequency of the sound wave.

The force diagrams of Figs. 2, 3, 4 and 6 are drawn for a given frequency and it is clear that the angular relationship of the forces depends on the frequency. Over a substantial range of frequencies the internal phase angle when screen 28 is present or i) where screen 28 is lacking will be shown subsequently in this specification to vary with frequency in the same proportion as the external phase angle, and that over this range of frequencies the directivity is independent of the fre quency. In one structure where screen 28 is missing, and for frequencies up to approximately 3000 cycles per second, directional action isobtained where the effective area of diaphragm II is 10 square centimeters, the mechanical compliance (inverse of stiffness) of the mounting of this diaphragm is 10- centimeters per dyne, the volume of cavity I6 is 10 cubic centimeters, the air in cavity I6 is at atmospheric pressure, the mass of diaphragm H and the drive unit I9 is a .12 gram, the mechanical compliance (inverse of stiffness) of link 22 is 4.2 10 centimeters per dyne, and the resistance of damping element 23 is 3,460 mechanical ohms. In this instance (1 is The effective area of the front diaphragm lfl is 5 square centimeters. The mass of diaphragm l9 and drive unit I! and the comthe cavity 29 in centimeters per dyne is analogous to an electrical shunt capacity C, in farads. The mechanical mass of diaphragm I0, drive unit I1, and crystal 24 in grams are lumped together and correspond to the electrical inductance Lc in henrys. The mechanical compliance of the mounting edge of diaphragm l0, crystal 24, and the compliance reflected by the air within cavity l5 upon the diaphragm I0, are-lumped together and correspond to the electrical capacity C3 in farads. The mechanical mass of diaphragm l l drive unit l9, and any effective mass of the dissipative element 23 in grams are lumped together and correspond to the electrical inductance L in hen rys. The mechanical compliance of the mounting edge of diaphragm II, the eflfective or equivalent compliance of dissipative element 23 and the air within cavity l6 (reflected upon the diaphragm) in centimeters per dyne are lumped together and correspond'to the electrical capacity C1 in farads. The mechanical resistance or damping in dyn-es per centimeter per second of element 23 corresponds to the electrical resist ance R" in ohms. For this to be true the damp"- ing of element 23 must be of a viscous character, which is to say that the force developed across it is dependent upon the velocity of the force. The mechanical compliance of link 22 in centimeters per dyne corresponds to the electrical shunt capacity C2 in farads. E, as already defined, is equal to PA and E is equal to PA' where Prand P are the sound pressures on diaphragms l0 and l I, and A and A are the areas thereof. The atmosphere is known to load the diaphragms. This gives rise to anadditional impedance term which is generally small compared with other elements in the circuit,.and it may be neglected. When such is not thecasa'however, this additional term sheuldbe Faken into account in the calculations.

Referring to the Patent No. 2,305,596, filed April 7, 194-1, issued on December 22,1942, under the name of Benjamin B. Bauer and assigned to the'same assignee'as the present invention, the electrical circuit illustrated in Fig. 8 thereof corresponds in form to the electrical circuit of Fig. '7- of this specification, and following the analysis there given cardioid directivity is obtained, that is,-.the voltagee across C3 and L3 in series is zero,

or the force tending to-deform crystal :24 is zero for rear sound incidence when c; isas already defined. j-is the mathematical symbolfor the expression J 1 Substituting the foregoing into Equation I there results V ilt noRwzLo If "itE-is 'define'd that Whi'chis the expression for the total capacitance of "C1 and C2 in series circuit and recalling that F180 and P180 are equal in magnitude but differ in phase by the angle wd'Cv, then Where [Mi /C,

represents the phase angle between P'iso and P480, the symbol 4 is the vectorial notation for phase angle-and all other quantities are as already defined. The factor and being pure numbers, Equation III is true only if 1+jwR"Cw LC The factors 1+ wRo w Lo =M (V) and Q 1 A (VI) Suppose for purposes of analysis that the compliance C1 were equal to infinity, that is to say that the stiffness of the mounting of diaphragm II and the air 'trappedin cavity I6 is reduced to zero, or so small as to be negligible. Then the factor reduces to unity for finite values of C2 and the areas of the diaphragms would be equal in this limiting case. Practically this condition is obtained if the compliance of the link 22 is much less than the combined compliance of the mounting of diaphragm H and cavity I6. Also under this assumption Where l+jwRCzw L'Cz is a unit vector operating at an angle very nearly proportional to frequency but with C2 only present, and Equation III becomes The vector diagram of Fig. 3 corresponds to Equations II and III, both being for rear sound incidence. Thus, E1 is force on diaphragm II, is equal to PA, and corresponds to Eiso; E is the force available at screen 28, is equal to PA, and corresponds to Eisc,xE being less than E due to the difference in the areas of the diaphragms and lagging behind E by an angle 4) equal to aid /C11 as previously pointed out; E1 is the force on the front of diaphragm l9 and lags behind E by an angle a represented by the factor 1+jwC'Rw LC, and E2 is the force shifted from the force (-E) by an angle (+a) represented by the factor 1+7'wRC"-w LC. In this case the force E2 is across C1 and C2 in series and it is only the force across C2 or E1 that opposes E1. Since a portion of the force applied is used to overcome C1 (to deflect diaphragm H and compress the air in cavity 16), it 'is necessary that the force E2 be greater than the force E or E1 in order that the component of force E2 across C2, namely E1, be equal to E1. E1 is the force transmitted to drive unit ll from diaphragm 'l l and is combined with E1, the force transmitted to drive unit I! from diaphragm IE), to .give the resultant force applied to crystal .24, which for degree sound incident must be zero.

Thus, due to the compliance of the mounting of diaphragm I l and the air in cavity 16, in order to have E1 and Ei'equal in magnitude, the force originating at diaphragm I must be greater than the force at diaphragm In by the factor If the compliance C1 is infinite, the areas of diaphragms l0 and II would be equal, and if the force diagrams of Figs. 2, 3, 4 and 5 were plotted, these would differ from those of the present fig ures in that the forces E, E1, E, E', and E1 would all be of equal magnitude. The angular relations would remain the same. By constructing diaphragms II and I0 such that their areas have the ratio defined by Equation VI, the compliance of the mounting of diaphragm U need not be neglected but may be taken account of to produce directivity over the complete frequency range. This result is attained by virtue of the factthat the pressure on diaphragm H is transmitted as a force and not as a pressure. Hence, increasing the area increases the force.

Also following the analysis given in the patent and from Equation III of this specification where wR'C' and wRC individually are considerably less than one J and from which it follows that w, the frequency term may be eliminated and (RC ROM (V I) The expression quarter of the sound wave. Thus, if d is equal approximately to two and one-half centimeters, cardioid directivity is obtained for all frequencies up to approximately 3,000 cycles per second. Since Cv, the velocity of sound, is a known constant for given conditions of temperature and pressure, the expression d/Cv is known for any Value of d which may be chosen. Then the values of R'C and RC may be determined in accordance with Equation IX and L and L may be determined from Equation IV.

It should not be assumed, however, that above 3000 cycles per second directional action ceases, because above the frequency where the transverse dimension of the microphone is a quarter 'wave length or greater, the instrument tends to become highly unidirectional in favor of sounds arriving from the front because of diffraction and the so-called baflle effect. With a transverse dimension of three centimeters, this effect begins at about 2500 cycles per second and directional action may therefore be obtained essentially throughout all of the important frequency range. 7

When the choice of microphone constants is made in accordance with the foregoing equations, the microphone will be insensitive to sound waves arising from the rear, that is, impinging perpendicularly upon diaphragm (direction of arrow B) and will have its greatest sensitivity to sound falling directly on diaphragm ||l (direction of arrow A). The sensitivity pattern will be heart shaped, i. e., the cardioid pattern shown in Fig. 8,, k=1.

The presence of screen 28 has some effect upon the directional properties of the microphone, it being responsible for the factor RC of Equation IX. It has been found, however, that by making the cavity 29 small, the principal effect of the screen is to dampen mechanical resonance of diaphragm l0. If screen 28 is completely eliminated, a slightly different choice of dimensions of dissipative element 23 and compliant link 22 is sufiicient to restore the desired direc tional properties. ,In this instance Equation IX reduces to Such a construction is advantageous in many instances since the cardioid directivity may be obtained for greater values of d. The constants may be so chosen that the viscosity of element 23 is sufficient to dampen the motions of diaphragm l0 and crystal 24 because of the coupling which attains through link 22.

In Fig. 5 another method of obtaining the dissipative component is shown. In this embodiment a screen 39 with fabric 4| attached thereto is placed behind diaphragm l the screen and fabric being placed very close to the diaphragm so that the volume of the cavity therebetween is very small. Hence the fluid motion of the air through the screen is, for all practical purposes, identical with the motion or displacement of the diaphragm. The screen 39 and fabric 4| have acoustical resistance which is the resistance to the flow of air therethrough and may be determined by measurin the pressure, in dynes per square centimeter, necessary to force a steady stream of air at the rate of one cubic centimeter per second through the screen. The acoustical resistance is then numerically equal to this pres sure and will provide the mechanical damping or dissipation which may be calculated by multiplying the acoustical resistance by the square of area of diaphragm l.

Correspondingly, screen 39 and fabric have acoustical mass or inertance and to obtain the mechanical mass the acoustical mass is also multiplied by the square of the diaphragm area. 0 The embodiment of Fig. 5 has a number of important advantages. It is known, for example, that compliance and inertance of air cavities and.

passages vary with the atmospheric pressure. For! instance, compliance varies inversely with variations in the atmospheric pressure and inertance varies directly with variations in the atmospheric pressure. On the other hand, the viscosity of air remains constant with atmospheric pressure through an unusually wide range of pressures. Likewise, viscosity remains practically constant with varying temperature. The embodiment of Fig. 5 employs the mass of diaphragm II and drive unit is and the mechanical compliance of link 22 for obtaining the reactive components of the phase shifting network at the same time it uses the acoustical resistance of screen 39 and fabric 4| for obtaining the dissipative element. In this manner a. structure is obtained producing the desired unidirectional effect which is subcensuses 1-5 'stantially independent tof the air pressure and temperature :and the microphone has unvarying unidirectional properties when used in. high Jaltitu'deilyin'g, for example.

Fig. 9 shows another manner of obtaining the dissipative effect producing damping of diaphragm .l l in order to obtain the necessary phase shift. In Fig. 9 the casing I3 is shown in fragmentary form together with drive unit [9, the drive unit bein attached on each side of casing 13 to imetallic diaphragms 3| and 32 by soldering or welding, for example. Diaphragms 3| and 32 are spaced from casing I3 by annular members 33 and '34 and cooperate therewith to define a chamber 35 filled with a suitable viscous substance :suoh'as'ia light oil or liquid silicone. The casing 13 between diaphragms 3i and 32 is provided with a number of small openings through which oil may flow. When the drive pin moves back and forth diaphragms 3| and 32 move therewith forcing the oil in chamber 35 to move back and forth through the openings in casing l3, thereby causing a dissipative action which provides the necessary dampin component. The compliance of diaphragms 3i and 32 becomes a part of the total compliance indicated as C" in Fig. 2 and the same analysis is applicable.

In Fig. another method of obtaining the requisite dissipative component is shown. The casing 13 is provided with a cylindrical portion 36 'which is adapted to be closed by a cover 3'! and flexible seals 40 and 21, chamber 36 being fillcd'with petroleum or silicone jelly or :a similar semi-solid substance. A disc 38 is attached to the drive unit I!) so that to-and-fro motions thereof produces t'o-and-fro motions of the disc in'the jelly-like substance and provides a satisfactory amount of dissipation for operation 'of the structure.

As already pointed out in Equation VIII the left-hand side, cud/Ct, represents the external phase difference, i. e., the phase difference between E and E which results from the time required for the sound wave to travel to the effective distance cl. The right-hand side, w(C"RCR), represents the internal phase difference, i. e., the difference between the phase shift the force E experiences in passing through the rear phase shifting network and the phase shift the force E experiences in passing through the acoustical screen 23 and cavity 29 to diaphragm Hi. If the quantity is is defined such that that is, as equal to the ratio of the internal phase difierence to the external phase difference, then the resulting response of the microphone 1, in polar coordinates, in terms of the angle of sound incidence, 0, is given by where p is proportional to the maximum pressure of the sound wave. As indicated in the patent referred to, this is the equation of the limacon. By substituting different values of R or different values of C in the expression for is and using this value of k in the equation of the limacon, the variation in directional response with the choice of the mechanical constants may be determined. When It equals one, that is, when Equation IX holds, a cardioid directional pattern results (Fig. 8). This is the directional characteristic frequently desired and 16" the one to which detailed consideration has been given. The microphone is capable of giving other responses. When 70 equals infinity the response is non-directional, i. e., it is a pressure responsive microphone. As It is made less than one, the microphone maintains its unidirectional property, or preferential response to sound of front incidence, but it has a definite, although a diminished, response to sound of rear incidence with zero response along two axes at an angle to the line of rear incidence. In the limiting case when lc equals zero, that is, when RC' equals RC, the microphone becomes a cosine bidirectional type (maximum response from front and rear and zero response from the sides).

Since d depends on the external shape of the microphone, and R and C are determined by the screen 28 and the volume of the cavity 29 respectively, the value of k is most conveniently changed by altering the product RC. All unidirectional characteristics of the microphone between the non-directional and the cosine bidirectional which are given by the equation of the limacon are obtained by varying is between zero and infinity. The value of infinity is obtained by eliminating the link 22; the value of zero is obtained by making the link 22 a rigid connection. By varying the value of the dissipation of element 23 or the resilience of link 22, the varying types of unidirectional response are obtained including the cardioid case. The spacing d, and consequently 01 may be varied by eliminating spacers l4 and casing 26 and movably mounting one of casings l2 and 53 relative to the other, such as by a rack and pinion. Varying this spacing will vary the directional pattern as already indicated.

One manner of obtaining variations in the compliance of link v22 connecting diaphragms l6 and In and in the amount of dissipation or damping associated with diaphragm l i is shown in Fig. 11. In this embodiment the general constructional features of the microphone are similar to those illustrated in Fig. 1 and the same reference numerals are used for corresponding parts. The structure of Fig. 11 differs from that of Fig. 1 in two respects, the first of these being that the fixed compliant link 22 of Fig. 1 has been replaced with a variable compliant link 6% and the second of these being that the block of dissipative material 23 of Fig. 1 has been replaced with an electromagnetic damping unit 67'.

Compliant link (it comprises a stirrup 68 connected to drive unit l9 and a resilient member or spring 89 connected to drive unit I'l. Stirrup 68 includes a pair of spaced apart members H and the member H being relatively rigid and the member '52 being relatively flexible. The resilient member as is rigidly attached to the end of arm ii, is slidably arranged in the corresponding end of arm 12, and is rigidly attached to the drive unit [1. Adjacent resilient member 69 an adjusting screw i3 is provided and is threadably received in cooperating threads in arm I! and through a hole in arm i2.

In the position shown, arms H and T2 are symmetrically disposed with respect to drive unit II. This is the normal position of arm 72 relative to arm H. Since the member 69 is resilient or flexible, it is evident that the link 66 has a certain value of compliance depending upon the relative. lengths of the portions of member 69 on each side of the drive unit ll. With the arms H and T2 symmetrically disposed about drive unit ll, the compliance of resilient member 69 may be so chosen that Equation IX is satisfied, that is to say, 7c=1 and the microphone has a cardioid response (for definite values of dissipation). By rotating adjusting screw it, the position of arm 12 may be changed from the position shown to any position up to those shown in broken lines. As arm '52 moves toward drive unit II, it is evident that the length of the resilient member 69 between drive unit I! and arm 12 is decreasing. Accordingly, the stiffness of resilient member 69 is increasing or the compliance thereof is decreasing. At the point where arm '52 is in contact with drive unit H, the compliance of link 65 has been reduced to zero. In other words, it is now a direct or rigid mechanical connection. As pointed out previously in this specification, when the link is rigid, k= and the microphone becomes a bidirectional or cosine law response microphone. Thus the type of microphone response may be changed from cardioid to cosine law merely by changing the position of the adjusting screw '53. Similarly, the adjusting screw may be varied to move arm 72 outward from its initial position to thereby decrease the stiffness of the link with a consequent reduction of the factor k and an approach of the response pattern toward the pressure response. After a definite value of R has been chosen, such as for cardioid response, changing the position of adjusting screw 13 will change the compliance of the link and thus change the value of C in equation X to give a certain value of 7c and consequently a different directional pattern of the microphone.

The dissipative unit 61 comprises a magnet 14 having a central pole l which maybe circular in cross-section and an outer pole 16 which may be annular in cross-section, the outer pole and the central pole defining an air gap between them within which a coil I1 is adapted to move. The magnet is arranged to be held rigidly relative to casing l3. The ends of coil ll are brought out of the casing along the diaphragm, one end thereof being connected to a resistor 18 and the other end being connected to a movable contact 19 for contacting resistor 18 at difierent points along its extent. By shifting contact 19, varying amounts of resistance may be placed in circuit with coil H. The coil Tl is mounted on a support which is rigidly connected to the drive unit It and thus the coil moves in its magnetic air gap whenever diaphragm ll moves or vibrates. As coil l1 moves in the magnetic air gap a voltage is generated therein which causes a current to flow through resistor E8, the amount of resistance in the circuit determining the magnitude of the current. The current flowing in coil ll sets up a magnetic field which interacts with the magnetic field of magnet 74, tending to oppose movement of diaphragm II or to dissi- Thus, whenever the value of C2 supplied by link 66 is varied, the amount of damping R supplied by unit 61 may be varied in order to satisfy the necessary relations. Moreover, the value of R. may be varied to satisfy Equation X to produce a directivity pattern other than the cardioid.

In one specific instance which has been found extremely desirable, k is made equal to the ratio 37/63. For this choice of 7c, the microphone has a unidirectional index of 14, that is, sounds coming at random from the solid angle encompassed by the front hemisphere will produce a respons 14 times as great as sounds coming at random from the solid angle encompassed. by the rear hemisphere. Whatever value one chooses for 70, however, the proper choice of circuit constants is given by Equations IV and X.

It is not necessary that the coupling means between the two diaphragms be merely compliant. It may include mass or inertance and resistance as well, that is, it may be a general impedance. In Fig. 15 one form of such a coupling connects the drive units I1 and IQ of the structure of Fig. l, for example. Connected to drive unit I9 is a cylinder 10, surrounding which is a ring Ha. of T shape in cross section. The ring Ha is connected by means of a stirrup 12a to drive unit H.

The cylinder i0 is held in position by a pair of flexible diaphragms 13a and 14a which are attached to the outer diameter of ring I la to form a chamber on each side of the central portion of the ring. The chambers are filled with liquid, such as a light oil, which is forced to move from one chamber to the other through the annular slit between the outside diameter of cylinder Ill and the inside diameter of the ring. The movement of the liquid through the narrow passage causes the presence of both resistance and inertance or mass. The compliance of the diaphragms 13a and 14a is the principal compliance of the system and serves to transmit the force from drive unit [9 to drive unit l1.

Following an analysis similar to that outlined for the structure of Fig. 1, cardioid directivity is obtained by the structure of Fig. 15 when the relationship of the constants is given by the expression 01+C'2 up to a frequency where d is not greater than one quarter wave length. In this expression C1 is the compliance of the mounting of diaphragm ll, R1 is resistance of the damping unit 23 (Fig. 1),C2 is the compliance of the diaphragms l3 and I4, and R2 is the resistance of the fluid flowing in the annular slit. The mass of diaphragm II is given by the expression and the inertance or mass of the fiuid flowing in the slit is given by the expression In order that directivity may be had at all frequencies, including the low frequencies, the ratio of areas of diaphragms H and I0 is given by the expression where these terms are as already defined. If the mounting compliance of diaphragm I I is negl1g1 ble then the areas A1 and A may be equal.

- '19 Another embodiment of my invention is illus trated in Fig. 12. In this embodiment the microphone comprises. a casing 44 of sound-impermeable material having two portions thereof on difierent diameters, the smaller portion being closed by a diaphragm 45 and the larger portion being closed by a diaphragm 46 thereby to define a closed cylindrical chamber Extending inwardly from the apex of diaphragmli5 and attached thereto is a drive unit 41, and extending inwardly from the apex. ofdiaphragm $5 and attached: thereto isa drive unit 48, the drive units being connected together by means of a. compliant link 49 which may be made of a spring, rubber, or elastomer similar to compliant link 2-2.. Supportedwithin. th casing 4 3 is a crystal 52 relatively rigidly connected to drive unit A? bya collar 50 whereby movements of diaphragm 45- are communicated thereto. Extending inwardly from casing 45 is a relatively rigidmember 53- adapted. to hold a dissipative. element 5 3 (-an elastomer for example) whichis connected to the drive unit fllltodampen themovements of diaphragm. 4 6

It will be seen that the microphone illustrated in Fig. 12 is'similar-to that of. 1 in that-two diaphragmsare coupledby. meansof a compliant link, and the modification of Fig. l2 differs from that of Fig. 1 in. that. diaphragms 45. and 46. in additionto link- 4eare coupled. by the.- compliance of the air within; chamber 5|, whereas. in.Fig. 1 diaphragmslfl-and H are. not coupled. by an air cavity. Compliantlink- 49. may be omitted, leaving only the coupling elfected by the air cavity,

without changing the unidirectional character of the microphone if compensatory changes are made'in theremaining microphone structure, as will be. subsequently explained.

The microphone of Fig. 12, while different. in construction: from, operates similarly to that of Fig-.1 inzthat the force arising from sound waves falling upon diaphragm 45 produces. one. force acting upon' crystal 52 through drive unit 41, and the force arising from sound waves falling uponr diaphragm 46 produces a. second force transmitted to the crystal. 52 through. drive pin 48, the deformation of the crystal, and'henceits output, being proportional to the resultant of the difference of these" forces. since the diaphragms oppose each other. The second force is made up of two parts, one of which is a force transmitted through link 58 and the other of which is a forceresul'ting'from the pressure transmitted through the air in cavity 5! and converted into a force at the underside of diaphragm 45. The mass of diaphragm 45 and the compliance of its mounting, the compliance of the air in cavity 5|, and thecomplian'ce of link 49, together with the damping of dissipative element 54, produce a phase shifting network by means of which the second force acting upon the crystal 52 is so shifted relative to the force-arising from sound waves fallingexternallyupon'diaphragm 45 that the microphone has maximum response for normal front incidence of sound (indicated by the arrow A) and minimum responsefor rear incidence of sound (indicated by the arrow B)'-. Other directional patterns may be obtained by proper selection of the network constants.

Since the output of this-microphone also is due to the deformation of the crystal 52, when there isno deformation of. crystal 52 there is novoltage output, and when the deformation of crystal 52 is at. a maximum there is maximum; vo ta '20 output. Accordingly, for this microphone to have a cardioid directional response, the elements thereof are arranged so that the deformation of crystal. 52. is zero when sound. is directly incident on the rear diaphragm.

In order to have'the deformation of crystal 52 equal to zero, it is evident that the resultant force acting on the crystal must be zero. Since sound pressures P and P of equal magnitude act on diaphragms 45 and 46 respectively producing forces E and E, these forces arising from the same sound wave, it is evident that the final combination of forces resulting from the forces E and E must be zero for sound of rear incidence. This may be visualized by the vector diagram of Fig. 13 which shows the relationship of forces for sound of rear incidence. Thus the vector E is the force due to sound falling on diaphragm 86, the sound coming in the direction of the arrow B, the'length of the vector E being equal to PA' where P is the pressure of the sound wave and A is the area of diaphragm 46. The sound wave continuing to travel also falls upon diaphragm 45 and exerts a force E equal to PA where P is the pressure of the sound wave and A is the area ofdiaphragm 45. Due to the time necessary for the sound wave to travel the effective distance d between diaphragms 45 and 46-, the force E lagsv behind the force E by phase angle which is equal to Hence, on the vector diagram, E is shown clock wise-from E by an angle Whereas the force on diaphragm 16 is opposed to the force on diaphragm 45, as for the microphone of Fig. 1, the force E is reversed and is shown as a force E on the diagram. The force E, even when reversed to E., does not combine directly with the force E, but due to the inherent characteristics of diaphragm 4'5, that is, its mass and the compliance of'its mounting, and dueto the char-' acteristics of the. means for transmitting the force from diaphragm 46 tov diaphragm 45, that is, the compliance of link 49, the compliance of the cavity 51' and the damping, of' the element 55, the force E1 finally transmitted through the link and through the cavity 5| to rear of diaphragm 45 and to the driving unit ll'has a phase angle relative to the force -E', this phase angle being designated as the internal phase angle of the. microphone. On the vector diagram, the shifted force E is shown as E2. Due to the compliance of diaphragm 46 a certain proportion of the force E" is consumed in deforming this element and thus is not available for. transmission to drive unit 47 either through the. air cavity 5| or the link 49. However, of. the force E2 a component E1? is transmitted to drivev unit 41,, and consequently combines with the force E to act on crystal 52. When the microphone is designed in accordance with the invention, the internal phase angle may be made equal to rod For sound of front incidence (direction of arrow A) the force diagram is of the same form as in Fig. 6. The force acting on diaphragm 45 may be illustrated as a vector E having the same magnitude as the vector E in Fig. 13. Then, due to the time'necessary for sound to travel the effective distance d, the force E, due to the sound falling on diaphragm is, may be illustrated as a vector E at a clockwise angle relative to the vector E. since cos :1 for front incidence. produced by the diaphragms are opposed to each other, the force E is acting reversely from the direction shown and accordingly is reversed to -E'. As indicated for the case of rear incidence of sound, due to the diaphragm plus the network coupling diaphragms 4% and t5, the force E2 lags behind the force -E by an internal phase angle which, in this case, is equal to the internal phase angle of Fig. 13 since the internal network has not been changed. In this case also a certain proportion ofthe force E or E2 is consumed in deforming diaphragm 5.5 and thus is not available for transmission to drive unit 41. However, there is a component of this force E1 equal in magnitude to the force E when the microphone is designed in accordance with the invention, which is transmitted to drive unit Al. The resultant Er of forces E11 and E deforms crystal 52 and produces the microphone output. Accordingly, it is evident that for sound of front incidence a force of definite value is availablev to deform crystal 52 and produce microphone output.

A microphone with cardioid directional properties up to 3000 cycles per second due to the network may be constructed in accordance with the invention having the following constants:

- The volume of cavity 5| equal to cubic centimeters; the area A of the rear diaphragm equal to 10 sq. centimeters; the acoustical compliance C4 of the air cavity equal to '7.1 10- cubic centimeters per dyne per square centimeter; the mechanical compliance C2 of the link equal to 1x10 centimeters per dyne; the mechanical compliance of the mounting of the rear diaphragm C1 equal to 1 X 10- centimeters per dyne; the mass of rear diaphragm and driving unit 48equal to .090 gram; the resistance of dissipative element 54 equal to 2470 ohms. The compliance of the mounting and mass of front diaphragm and drive unit 41 may be equal to those of the corresponding rear elements; the area of the Referring to Fig. 14, E is analogous to the force produced by the pressure P of sound waves falling In this case also, since the forces on diaphragm and is equal to PA where A is the area of the diaphragm. E is analogous to the force produced by the pressure P of sound waves falling on diaphragm 4B andis equal to P'A where A is the area of this diaphragm. The mechanical mass of diaphragm 45, drive unit 47 and crystal 52 in grams lumped together, are analogous to the inductance L3, and the mechanical compliance of the mounting of diaphragm 65 is analogous to the electrical capacity C3. The mass of the diaphragm 45, of the drive unit 48, and the equivalent mass of dissipative unit *54 in grams may be lumped together and are analogous to the electrical inductance L1. The mechanical resistance of the dissipativeelement 54 is analogous to the electrical resistance R. The mechanical compliance of the mounting of diaphragm 46, and the equivalent compliance of the dissipative element 54 may be lumped together and are analogous to the electrical capacity C1. The compliance of link 49 is analogous to the electrical capacity C2, and the compliance of the air within the cavity 5| is analogous to an electrical capacity C4.

The two compliant elements, link es and the air in cavity 5|, are factors in coupling the vibrations of diaphragms l5 and 46, and may be considered to be acting separately, and are shown coupled by idealized transformers 55, 55a, 56 and 56a, including respectively windings 5? and 58, 59 and 6|, {i2 and 63, and 54 and 65. The turn ratios of windings 51' to 58 and 62 to 63 are as one to one, the turn ratio of winding 59 to Winding 6| is as A to one, and the turn ratio of winding 64 to winding 55 is as one to A, A and A being the areas of diaphragms 45 and 46 respectively. Thus the mechanical compliance of the link 49 (C2) is directly coupled to the diaphragms and the acoustical compliance of the air in cavity 5| (C4) is coupled thereto through transformers having a ratio of one to A and one to A respectively.

The treatment of the air coupling of cavity 5| (C4) and the link 49 (C2) coupling the diaphragms through transformers having transformation ratios corresponding to the areas of the diaphragms and having transformation ratios of unity is a consequence of the fact that the link 49 transmits a force and the air in cavity 5| transmits a pressure. When pressure is exerted on the exterior of diaphragm 46, there is a total force produced equal to product of the pressure and area. This force decreased by the amount needed to overcome the compliance of themounting of diaphragm 46 is transmitted in proportionate amounts as a pressure through the air in cavity 5| and as a force through link 49 to diaphragm :35 and drive unit 41, depending on the relative compliance of these elements.

Since link 49 transmits its proportionate amount of force directly without any change in its value, it is represented as coupling the diaphragms through one to one ratio transformers. However, the proportion of force transmitted by the air appears as a pressure inside of the casing, and while this proportionate part of the force at diaphragm as is equal to pressure inside of the casing multiplied by the area of the diaphragm, only the inside pressure is transmitted to diaphragm 45 where the force is this pressure multiplied by the area of diaphragm d5. Due to link E9 the force transmitted from one diaphragm to the other depends on the diaphragm areas, and since the pressure in cavity 5| has an average value, the air is shown coupling the diaphragms through transformers having the areas as ratios of transformation.

' For cardioid directivity the resultant force for sound of rear incidence tending to deform crystal 52 must equal zero, as pointed out previously, or the voltage e across L303 must be equal to zero. Analyzing the circuit of Fig 14 and imposing the condition that the response (voltage e) be zero for rear or 180 sound incidence, the following relation is obtained Eiso is the voltage or force arising from sound pressure on diaphragm 46, it being equal to PA and E180 is the force of sound pressure on diaphragm 45 and is equal to PA. It should be noted that C" and C2 are units of mechanical compliance, centimeters per dyne, while C4 is given in units of acoustic compliance, cubic centimeters per dyne per square centimeter.

Since diaphragms 45 and 4B are spaced apart, there is a phase difference between the external sound pressures exerted thereon, as has already been pointed out, equal to XIV - 1 Cl (X From the expression A C, If 1 o:

it is evident that the ratio of the diaphragm areas depends upon the ratio of the compliance of the mounting of diaphragm 46 and the compliance of link 49.

Where the mounting compliance of diaphragm 46, C1, is very large compared to the compliance C2 of link 49 (compliance C1 equal to infinity or the stiffness of link C2 is great compared to the stiifness of diaphragm 4%) the ratio of areas becomes equal to unity. In other words, to have equal diaphragm areas, the compliance of diaphragm 46 must be equal to infinity or unidirec- .tivity at l w frequenc es wil not cc Where the stilfness of diaphragm 46 may not be ignored in obtaining unidirectivity at all frequencies, the area of this diaphragm may be increased as determined by the relation given to compensate therefor. As explained in connection with the microphone of Fig, 1, link 49 transmits a force. When the area of diaphragm 46 is increased, the total force available is increased and the proper portion of the increase is transmitted to diaphragm 45 to compensate for the force consumed in deforming diaphragm 46. The links C2 may be omitted in some instances leaving only the air in cavity 5i coupling diaphragms 45 and 46. When this occurs thereis only the pressure of the air in cavity 5| to transmit force from diaphragm 46 to diaphragm 45. Increasing the area of diaphragm 45, then, has no effect and there could be unidirectivity at all frequencies only if the stillness of diaphragm 46 can be neglected. The actual evaluation of microphone constants to compensate for the assumption that the compliance of diaphragm 46 is infinite, or that the compliance of link 49 is infinite may be understood by a reference to Equations XV and XVI.

From Equation X111 for unidirectional operation and for the instance where the expression oRC is considerably less than 1, one may write the expression this relationship the factor or may be eliminated giving CTR 0 Since this expression must be true for cardioid directional operation, if R. has been chosen, the factor C must remain the same since is a constant for any microphone. Accordingly, if the values of any of C1, C2 and C4 are changed, the remaining values must be made to conform to this relationship.

The compliance C1 of the rear diaphragm is a factor in the equations and is taken account of by the link 49 and the increased area of diaphragm 46 to produce directivity at all frequencies up to those for which the effective distance d is not greater than one-quarter of the sound frequency. In instances Where the compliance of the rear diaphragm is high enough to be neglected, which is true only above the lower frequencies, the microphone may have directional operation without the link 49 and with the areas of the two diaphragms equal providing R and C4 are properly chosen as outlined above.

While the description relating to Fig. 12 has been with reference to cardioid directivity, it will be understood that this is exemplary only. The various factors of R, C2 d may be made in accordance as outlined in connection with Figs. 1, 5 and 11 to obtain bidirectional response, pressure response or variations therefrom. Moreover, as outlined, the directional pattern may be made 25 adjustable by providing means to adjust the constants;

While particular embodiments of the invention have been shown, it will be understood, of course, that the invention is not limited thereto since many modifications may be made, and it is therefore contemplated by the appended claims to cover any such modifications as fall within the true spirit and scope of the invention.

Having thus described the invention, what is claimed and desired to be secured by Letters Patent is:

1. A directional sound translating device comprising first and second diaphragms adapted to vibrate relative to each other and defining an enclosed chamber containing a gaseous medium,

said diaphragms being spaced from each other thereby to effect a phase difference between the force of sound waves striking one of said diaphragms and the force of said sound waves striking the other of said diaphragms, means for transforming vibrations into electrical variations, a stiff link for transmitting the force arising at said one diaphragm to' said transforming means,

relative to each other,- said diaphragms being spaced apart from each other thereby to effect a phase difference between the force of sound waves striking one of said diaphragms and the force of said sound waves striking the second one of said diaphragms, means for transforming vibrations into electrical variations, a stiff link for transmitting the force arising at said one diaphragm to said transforming means, compliant mechanical link means for transmitting a function of the force arising at said second diaphragm to said transforming means, and means for damping vibrations of said second diaphragm, said compliant mechanical link means, said damping means, and said diaphragm producing a phase shift of the force arising at said second diaphragm having a certain phase relationship to the force arising at said one diaphragm.

3. A directional sound translating device comprising first and second diaphragms adapted to vibrate relative to each other, said diaphragms being spaced apart from each other thereby to effect a phase difference between the force of sound waves striking one of said diaphragms and the force of said sound waves striking the other of said diaphragms, means for transforming vibrations into electrica1 variations, phase shifting means including said second diaphragm for producing a phase shift between the forces acting on the two sides of said first diaphragm, and means for transmitting the resultant of said forces acting on the two sides of said first diaphragm to said transforming means.

4. A directional sound translating device comprising a first diaphragm having a certain surface area and compliance and adapted to vibrate in response to the forces exerted on its two sides, one of said two sides being substantially exposed whereby sound waves incident thereon exert a force, casing means, a second diaphragm having a certain surface area and compliance spaced from said first diaphragm vibratable relative thereto and having one side substantially exposed whereby sound waves incident thereon exert a force, said casing means and said diaphragms defining an enclosed chamber containing an elastic medium, a transducing element relatively rigidly connected with only said first diaphragm, a compliant link interconnecting said diaphragms, and means for damping vibrations of said second diaphragm, said medium and said link transmitting a force from said second diaprising a first diaphragm having a certain surface area and compliance and adapted to vibrate in response to the forces exerted on its two sides, one of said two sides being substantially exposed whereby sound waves incident thereon exert a force, casing means, a second diaphragm having a certain surface area and compliance spaced from said first diaphragm vibratable relative thereto and having one side substantially exposed whereby sound waves incident thereon exert a force, said casing means and said diaphragms defining an enclosed chamber containing an elastic medium, a transducing element relatively rigidly connected with only said first diaphragm, a compliant link interconnecting said diaphragms, and means for damping vibrations of said second diaphragm, said medium and said link transmitting a force from said second diaphragm to the other side of said first diaphragm, the surface area of said second diaphragm being greater than the surface area of said first diaphragm to compensate for the stiffness of said second diaphragm, the ratio of the area of said second diaphragm to said first diaphragm being substantially equal to unity plus the ratio of link compliance to the compliance of said second diaphragm.

6. A directional sound translating device comprising a pair of spaced apart diaphragms adapted to vibrate relative to each other and defining a closed chamber containing an elastic medium, means for transforming vibrations into electrical variations relatively rigidly connected to one of said diaphragms, means for damping vibrations of the other one of said diaphragms, means including a compliant link and the elastic medium in said chamber for coupling said diaphragms.

7. A directional sound translating device comprising a first diaphragm adapted to vibrate in response to the forces exerted on its two sides, one of said two sides being substantially exposed whereby sound waves incident thereon exert a force, means including a second diaphragm spa'cedfrom said first diaphragm vibratable relative thereto and having one side substantially exposed whereby sound waves incident thereon exert a force, said means and said diaphragms defining an enclosed chamber containing an elastic medium, a transducing element relatively rigidly connected with only said first diaphragm, a compliant link interconnecting said diaphragms, and means for damping vibrations of said second diaphragm, said medium and said link transmitting a force to the other side of said first diaphragm.

8. A directional sound translating device comprising a first diaphragm adapted to vibrate, in

27 response to the forces exerted on its two sides, one of said two sides being substantially exposed whereby sound waves incident thereon exert a force, means including a second diaphragm spaced a fixed distance from said first diaphragm vibratable relative thereto and having one side substantially exposed whereby sound waves incident thereon exert a force, said means and said diaphragms defining an enclosed chamber containing an elastic medium, a transducing element relatively rigidly associated with only said first diaphragm, a resilient link interconnecting said diaphragms, and means for damping vibrations of said second diaphragm, said medium and said link transmitting a force from said second diaphragm to the other side of said first diaphragm, said link, said medium, said damping means and said second diaphragm constituting a phase shift network for shifting the phase of the force on said other side of said first diaphragm relative to the force on said second diaphragm by a value equal to the phase difference between sound pressures of a sound wave traveling said distance.

9. A directional sound translating device comprising a first diaphragm adapted to vibrate and defining at least a portion of one side of a closed chamber containing an elastic medium, a transducing element relatively rigidly connected to said first diaphragm, a second diaphragm adapted to vibrate relative to said first diaphragm and defining at least a portion of one side of another closed chamber containing an elastic medium, each of said diaphragms being adapted to have sound waves fall thereon, and a compliant link interconnecting said first and second diaphragms.

10. A directional sound translating device comprising a first diaphragm adapted to Vibrate and defining at least a portion of one side of a closed chamber containing an elastic medium, a transducing element relatively rigidly connected to said first diaphragm, a second diaphragm adapted to vibrate relative to said first diaphragm and defining at least a portion of one side of another closed chamber containing an elastic medium, each of said diaphragms being adapted to have sound waves fall on one side thereof, a compliant link transmitting a force from said second diaphragm to the other side of said first diaphragm, and means for damping vibrations of said second diaphragm, said damping means, said compliant link, said second chamber and said second diaphragm constituting phase shifting means for shifting the phase of the force exerted on said other side of said first diaphragm relative to the force exerted on said one side of said second diaphragm.

11. A directional sound translating device comprising a first diaphragm having a certain surface area and compliance adapted to vibrate and defining at least a portion of one side of a closed chamber containing an elastic medium, a transducing element relatively rigidly connected to said first diaphragm, a second diaphragm having a certain surface area and compliance adapted to vibrate relative to said first diaphragm and defining at least a portion of one side of another closed chamber containing an elastic medium, said first and second diaphragms being spaced apart from each other a fixed distance and being adapted to have sound waves fall on the outside thereof, and a compliant link coupling said first and second diaphragms, the surface area of said second diaphragm being greater than the surface area of said first diaphragm to compensate for the stiffness of said second diaphragm, said sec- 28 ond diaphragm being greater in area in propor tion to the ratio of the compliance of said link and said second diaphragm.

12. A directional sound translating'device comprising a first diaphragm having a certain surface area and compliance adapted to vibrate and defining at least a portion of one side of a closed chamber containing an elastic medium, a transducing element relatively rigidly connected to said first diaphragm, a second diaphragm having a certain surface area and compliance adapted to vibrate relative to said first diaphragm and defining at least a portion of one side of another closed chamber containing an elastic medium, said first and second diaphragms being spaced apart from each other a fixed distance and being adapted to have sound waves fall on the outside thereof, elastic means coupling said diaphragms thereby to transmit a force from said second diaphragm to the other side of said first diaphragm, and means for damping the vibrations of said second diaphragm, the surface area of said second diaphragm being greater than the surface area of said first diaphragm to compensate for the stiffness of said second diaphragm, the ratio of the area of said second diaphragm to said first diaphragm being substantially equal to unity plus the ratio of the compliance of said elastic means to the compliance of said second diaphragm, said damping means, said second diaphragm, and said other chamber constituting phase shifting means for shifting the phase of the force transmitted to said other side of said first diaphragm relative to the force exerted on the outside of said second diaphragm by a value substantially equal to the phase angle between pressures in a sound wave traveling said distance.

13. A directional sound translating device comprising a first diaphragm having a certain surface area and compliance, a second diaphragm having a certain surface area and compliance, said first and second diaphragms being spaced apart from each other a fixed distance, and a link having compliance coupling said diaphragms, the surface area of said second diaphragm being greater than the surface area of said first diaphragm to compensate for the stiffness of said second diaphragm, said second diaphragm being greater in area in proportion to the ratio of the compliance of said link and said second diaphragm.

14. A directional sound translating device comprising a first diaphragm having a certain surface area and compliance, a second diaphragm having a certain surface area and compliance, said first and second diaphragms being spaced apart from each other a fixed distance, and a link having compliance coupling said diaphragms, the surface area of said second diaphragm being greater than the surface area of said first diaphragm to compensate for the stiffness of said second diaphragm, the ratio of the area of said second diaphragm to said first diaphragm being substantially equal to unity plus the ratio of link compliance to the compliance of said second diaphragm.

15. A directional sound translating device having a pair of spaced apart diaphragms, a transducing device connected to one of said diaphragms for converting vibrations thereof into electrical variations, and means including a compliant link between said one and the other of said diaphragms for transmitting forces therebetween, the other of said diaphragms being greater in surface area than said one diaphragm, the

29 ratio of the surface area of said other diaphragm to saidone diaphragm being greater than unity and sufficient to compensate for the stiffness of said other diaphragm over a substantial range of sound frequencies.

16. A directional sound translating device having a pair of spaced apart diaphragms, a transducing device connected to one of said diaphragms for converting vibrations thereof into electrical variations, and means including a compliant link between said one and the other of said diaphragms for transmitting forces therebetween, the other of said diaphragms being greater in surface area than said one diaphragm, the ratio of the surface area of said other diaphragm to said one diaphragm being substantiolly equal to one plus the ratio of the stiffness of said compliant link and the stiffness of said other diaphragm.

17. A directional sound translating device comprising a first diaphragm having a certain surface area and compliance and producing a force from sound waves thereon, a second diaphragm spaced from said first diaphragm vibratable relative thereto and producing a force from sound waves falling thereon, said second diaphragm having a certain surface area and compliance, transducing means relatively rigidly connected to said first diaphragm, means including compliant means coupled to said second diaphragm for subtractively transmitting said forces to said transducing means, the surface area of said second diaphragm being greater than the surface area of said first diaphragm to compensate for the stiffness of said second diaphragm, the ratio of the area of said second diaphragm to said first diaphragm being substantially equal to unity plus the ratio of the compliance of said compliant means to the compliance of said second diaphragm.

18. A directional sound translating device comprising a first diaphragm having a certain surface area and compliance and producing a force from sound waves thereon, a second diaphragm having a certain surface area and compliance spaced from said first diaphragm vibratable relative thereto and producing a force from sound waves falling thereon, transducing means relatively rigidly connected to said first diaphragm, compliant means coupling said diaphragms, and means for varying the compliance of said compliant means, the surface area of said second diaphragm being greater than the surface area of said first diaphragm to compensate for the stiffness of said second diaphragm, the ratio of the area of said second diaphragm to said first diaphragm being substantially equal to unity plus the ratio of the compliance of the compliant 30 means to the compliance of said second diaphragm.

19. The invention according to claim 3 characterized in that the phase shifting means for producing a phase shift between the forces acting on the two sides of the first diaphragm, in addition to the second diaphragm, comprises a link having mechanical impedance including compliance between the first and second diaphragms.

20. The invention according to claim 3 characterized in that the phase shifting means for producing a phase shift between the forces acting on the two sides of the first diaphragm, in addition to the second diaphragm, comprises a link having mechanical impedance including inertance, compliance, and non-gaseous fluid friction.

21. The invention according to claim. 2 characterized in that the means for damping vibrations of the second diaphragm comprises fluid friction means.

22. The invention according to claim. 2 characterized in that the means for damping vibrations of the second diaphragm comprises a relatively movable vane and viscous medium.

23. The invention according to claim 2 characterized in that the means for damping vibrations of the second diaphragm comprises semi-fluid solid medium means.

24. The invention according to claim 2 charac- I terized in that the means for damping vibrations of the second diaphragm comprises electromagnetic means.

BENJAMIN B. BAUER.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 687,999 Liebrich Dec. 3, 1909 1,551,105 Hayes Aug. 25, 1925 1,775,453 Foley Sept. 9, 1930 1,814,458 Steimberg July 14, 1931 2,184,247 Baumzweiger Dec. 19, 1939 2,198,424 Baumzweiger Apr. 23, 1940 2,305,596 Bauer Dec. 22, 1942 2,305,597 Bauer Dec. 22, 1942 2,305,593 Bauer Dec. 22, 1942 2,305,599 Bauer Dec. 22, 1942 2,474,197 Dimmick June 21, 1949 FOREIGN PATENTS Number Country Date 15,084 7 Netherlands Aug. 16, 1926 272,263 Great Britain June 9, 1927 

